Gambler's fallacy vs. Theory of Probablity

In Tharp's "Trade Your Way to Financial Freedom", he talked about Gambler's fallacy. Using an example of a game played by 40 Ph.D.s,(each of whom were given $1,000 to play 100 trials and their winning chance is 60 percent), he got the conclusion that only 2 of them made money finally because of wrong position sizing. He said that suppose the first three bets are losers and you bet $100 each time. You would think :"Well, I've got three losses in a row and it's time for a win." So you bet more for the fourth time, which he said you've fallen into gambler's fallacy because the fourth trade still has the winning probability of only 60 percent. I was just wondering why probablity theory doesn't work here. According to probability theory, since each trade has two results--winning or losing, the prob. of the fourth consecutive loss should be (1-0.6)*(1-0.6)*(1-0.6)*(1-0.6) instead of (1-0.6). And honestly if I were in that game, I would also bet more after three losses in a row. Also, Tharp seems to believe that 10 losses in a row in the market is very natural, which again contradicts to prob. theory. Any thoughts or explainations will be greatly appreciated.

The futures markets have a non-repeating pattern i.e. when
futures decline big the next day and the following this
pattern is unlikely to repeate. I think the key is weather
the trials are independent or based on a continued flow of
the same pattern. It's naive to draw paralel in coin toss
and continued decline of one index for example. The whole
idea of a chaos move (big news or hype) and professionals
fading such move. According this theory they are always
wrong because the next day and the day after it should be based on the new probability. You are right, this is wrong.

Your example is classic misinterpretation of statistics. In this case, any single event always has a probability of 60% success and 40% failure. Chance of four failures in a row is (1-.6)^4 like you described. But, (and here is the key) this only applies BEFORE any of the events have happened. The chance that the next event is a failure is only 40%. But the chance that the next four events in a row are a failure is 40% x 40% x 40% x 40%.

In the case described by Tharp, the PhD falsely believe that the past three events influence the fourth, which they won't. If you could step back in time to before the first three events happened, then the chance that all four events are failures is very low. But since each event is independent of each other, probability only works for future events.

Its funny that you can give 40 traders a system that at the very least will produce a min. of 50% return on equity at the end of the 100 trials and still they can not make money using it, and these are PHD's

Most traders do not undertsand that within any edge there is a natural distribution of wins and losses.............

While it is highly improbable you could actualy take 40 straight losses.....

It seems odd that only 2 out of 40 participants would make money if the chance of winning is 60%. In a positive outcome experiment, regardless of their methodology, over that many trials chance should work it's magic and more players should win than lose. Even if their flawed methodology leads them to bet the farm after several losing attemps, there is still a positive expectation value for that trial.

I guess it would depend whether it was a game that involved skill (which the didn't have) or purely a random outcome game.

The reason almost everyone lost money is because people would vary their betting size from game to game. With a flat betting size, one can expect to make money over time since the odds are over 50%. But if you bet too much of your capital and you happen to lose that game (40% chance), then you might not be able to risk the same amount the next game. This is what destroys you.

Skiley,
There are two ways to look at the game the PHd's played. Say you have a bag of marbles and 60 are black (winner), while 40 are red (loser). If you keep each marble out of the bag after each draw, and let's say you draw several losers in a row, then yes, your odds of picking a winner would slowly increase with each losing draw. (Obviously, because there are now less losers to choose from). BUT...if you put each marble back in the bag after each draw then the odds will always stay the same. There will always be a 60% chance of picking a winner and a 40% chance of picking a loser with each draw. This is how the PHd's played the game.

The point is that it really doesn't matter how many losers you pull in a row because if the game has a positive expectancy then you'll always win in the long run. I read Tharps book too and decided to play my own marble game. The results amazed me. I played several games of 100 draws and I always came out ahead. In one game I had as many as 12 losers in a row. But in the end I was always very close to the 60%. It was a real eye opener.

Mark Douglas also talks about this in "Trading in the Zone". He says you must think like a casino. If you truly have an exploitable edge, then coupled with risk management, position sizing, and a good profit taking strategy, you'll always win over the long term.

The problem that traders have is they get too emotional with the losers. Imagine if someone at a casino was playing roullette and kept betting on red every time. Now imagine that there was a huge streak of reds rolled. Would the casino manager come and stop the game and say, "I'm sorry we've lost too much money against you, we're going to stop this game now"? Of course not. They don't care how many times you win. You may win today, or tomorrow, or all week, but over a long enough period of time, the casino will ALWAYS win. They have to. It's a positive expectancy game for them. There are more winning marlbes in their bag than in yours.

The other problems traders have according to Mark Douglas is that they attatch personalities to the markets or to stocks that don't have personalities. Let's say you've discovered a profitable set-up in NVDA. Over a large sampling and backtesting you've discovered that this setup will produce a winner 70% of the time. Well unfortunately the last 5 times you've taken it you've lost. The sixth time you see the setup, you hesitate. Instead of putting your faith in the probability of the setup you start thinking of the last 5 losers. So instead of taking it, you say "Oh hell with it, I hate NVDA. That stupid stock always burns me, I'm going to play something else". Well, that's of course usually the time it works and would have made you a lot of money.

Final thought. When you increase your bet size after a loser you're using a Martingale strategy. Theoretically it works but it doesn't work in real life. If you had an unlimited bank roll and the right game it would work. With roullette for example, if you kept doubling your bet after each loser then eventually it's going to hit your color and you'll get all your money back. The problem is that casinos know this works and that's why they put a high bet limit on their games. The other problem is that it multiplies so fast against you. If you started out betting $10 and you lost 7 times in a row you'd be risking $1,280 just to make back your $10. 10 losers in a row and you'd be betting $10,240 and on and on. It gets to the point where you're risking insane amounts of money just to break even.

The correct thing to do is to increase your bet size when you're winning and reduce when your losing. Again, one more thing that's a lot easier said than done and very unnatural.

Excellent!
Huby, I still have one question though. You said:"The correct thing to do is to increase your bet size when you're winning and reduce when your losing.", which is the Anti-martingale strategy. What's the idea behind that? Why should you expect to win after winning while you shouldn't expect to win after losing?
Thank you very much for your help!

Excellent thread....I am very interested in statistics. (Funny how I hated it and paid no attention in college) Does anyone here use statistics to place trades? Does backtesting a system on a program like tradestation give probabilities? (I have never used a program like Tradestation...so I am curious on its effectiveness)

One trader at my office....well actually he trades through my office but he is NEVER really there. You see he plays golf everyday. At 3 o'clock everyday he faxes in his trades. He usually has 20 to 30 positions. These positions are usually around 200-1000 shares. He trades pairs and he makes SIZE. From what I hear he sets up his own programs which calculate deviations. Some days he makes 20 grand and some days he loses 10 grand...BUT at the end of the month he always comes out on top.

A few months ago I toyed around with a spread trading, sometimes market-neutral strategy. Basically I didn't have the experience and the software knowledge to make it work. But eventually I will set up my own "system" based on correlations and probabilies to trade this way.

OK, I get it Htrader. Say each trader bet 100% of their money every time. It would be *highly* unlikey that anyone would have a run which lasted through the 100 events. They would wash out with nothing

In a game such as this, with each individual event being win all/lose all, how do you calculate your bet size to maximize your profit while minimizing your risk?

Another thing, if you were to consider an infinite number of betters, and imagine they did bet 100% each event, mathematically would there still be a positive expectation? Because eventually there would be a run of 100 events, and that individual would win an astronomical ammount.